We propose to generalize the volume conjecture to knotted trivalent graphs and we prove the conjecture for all augmented knotted trivalent graphs. As a corollary we find that for any link there is an arithmetic link containing for which the volume conjecture holds.
"The volume conjecture for augmented knotted trivalent graphs." Algebr. Geom. Topol. 9 (2) 691 - 722, 2009. https://doi.org/10.2140/agt.2009.9.691